Core_DOM/Core_DOM/common/monads/CharacterDataMonad.thy

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(***********************************************************************************
* Copyright (c) 2016-2018 The University of Sheffield, UK
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* SPDX-License-Identifier: BSD-2-Clause
***********************************************************************************)
section\<open>CharacterData\<close>
text\<open>In this theory, we introduce the monadic method setup for the CharacterData class.\<close>
theory CharacterDataMonad
imports
ElementMonad
"../classes/CharacterDataClass"
begin
type_synonym ('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr,
'shadow_root_ptr, 'Object, 'Node, 'Element, 'CharacterData, 'result) dom_prog
= "((_) heap, exception, 'result) prog"
register_default_tvars
"('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr,
'Object, 'Node, 'Element, 'CharacterData, 'result) dom_prog"
global_interpretation l_ptr_kinds_M character_data_ptr_kinds
defines character_data_ptr_kinds_M = a_ptr_kinds_M .
lemmas character_data_ptr_kinds_M_defs = a_ptr_kinds_M_def
lemma character_data_ptr_kinds_M_eq:
assumes "|h \<turnstile> node_ptr_kinds_M|\<^sub>r = |h' \<turnstile> node_ptr_kinds_M|\<^sub>r"
shows "|h \<turnstile> character_data_ptr_kinds_M|\<^sub>r = |h' \<turnstile> character_data_ptr_kinds_M|\<^sub>r"
using assms
by(auto simp add: character_data_ptr_kinds_M_defs node_ptr_kinds_M_defs
character_data_ptr_kinds_def)
lemma character_data_ptr_kinds_M_reads:
"reads (\<Union>node_ptr. {preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t node_ptr RObject.nothing)}) character_data_ptr_kinds_M h h'"
using node_ptr_kinds_M_reads
apply (simp add: reads_def node_ptr_kinds_M_defs character_data_ptr_kinds_M_defs
character_data_ptr_kinds_def preserved_def)
by (smt node_ptr_kinds_small preserved_def unit_all_impI)
global_interpretation l_dummy defines get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a = "l_get_M.a_get_M get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a" .
lemma get_M_is_l_get_M: "l_get_M get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a type_wf character_data_ptr_kinds"
apply(simp add: get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_type_wf l_get_M_def)
by (metis (no_types, hide_lams) NodeMonad.get_M_is_l_get_M bind_eq_Some_conv
character_data_ptr_kinds_commutes get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def l_get_M_def option.distinct(1))
lemmas get_M_defs = get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def[unfolded l_get_M.a_get_M_def[OF get_M_is_l_get_M]]
adhoc_overloading get_M get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
locale l_get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_lemmas = l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
begin
sublocale l_get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas by unfold_locales
interpretation l_get_M get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a type_wf character_data_ptr_kinds
apply(unfold_locales)
apply (simp add: get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_type_wf local.type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a)
by (meson CharacterDataMonad.get_M_is_l_get_M l_get_M_def)
lemmas get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ok = get_M_ok[folded get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def]
end
global_interpretation l_get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_lemmas type_wf by unfold_locales
global_interpretation l_put_M type_wf character_data_ptr_kinds get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
rewrites "a_get_M = get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a" defines put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a = a_put_M
apply (simp add: get_M_is_l_get_M l_put_M_def)
by (simp add: get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def)
lemmas put_M_defs = a_put_M_def
adhoc_overloading put_M put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
locale l_put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_lemmas = l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
begin
sublocale l_put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas by unfold_locales
interpretation l_put_M type_wf character_data_ptr_kinds get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a
apply(unfold_locales)
using get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_type_wf l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a.type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a local.l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_axioms
apply blast
by (meson CharacterDataMonad.get_M_is_l_get_M l_get_M_def)
lemmas put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ok = put_M_ok[folded put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def]
end
global_interpretation l_put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_lemmas type_wf by unfold_locales
lemma CharacterData_simp1 [simp]:
"(\<And>x. getter (setter (\<lambda>_. v) x) = v) \<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> h' \<turnstile> get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr getter \<rightarrow>\<^sub>r v"
by(auto simp add: put_M_defs get_M_defs split: option.splits)
lemma CharacterData_simp2 [simp]:
"character_data_ptr \<noteq> character_data_ptr'
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr' getter) h h'"
by(auto simp add: put_M_defs get_M_defs preserved_def split: option.splits dest: get_heap_E)
lemma CharacterData_simp3 [simp]: "
(\<And>x. getter (setter (\<lambda>_. v) x) = getter x)
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr' getter) h h'"
apply(cases "character_data_ptr = character_data_ptr'")
by(auto simp add: put_M_defs get_M_defs preserved_def split: option.splits dest: get_heap_E)
lemma CharacterData_simp4 [simp]:
"h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr getter) h h'"
by(auto simp add: put_M_defs ElementMonad.get_M_defs preserved_def
split: option.splits dest: get_heap_E)
lemma CharacterData_simp5 [simp]:
"h \<turnstile> put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr getter) h h'"
by(auto simp add: ElementMonad.put_M_defs get_M_defs preserved_def
split: option.splits dest: get_heap_E)
lemma CharacterData_simp6 [simp]:
"(\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
apply (cases "cast character_data_ptr = object_ptr")
by(auto simp add: put_M_defs get_M_defs ObjectMonad.get_M_defs NodeMonad.get_M_defs
get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def preserved_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
bind_eq_Some_conv split: option.splits)
lemma CharacterData_simp7 [simp]:
"(\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
apply(cases "cast character_data_ptr = node_ptr")
by(auto simp add: put_M_defs get_M_defs ObjectMonad.get_M_defs NodeMonad.get_M_defs
get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def preserved_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
bind_eq_Some_conv split: option.splits)
lemma CharacterData_simp8 [simp]:
"cast character_data_ptr \<noteq> node_ptr
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
by(auto simp add: put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def NodeMonad.get_M_defs
preserved_def split: option.splits dest: get_heap_E)
lemma CharacterData_simp9 [simp]:
"h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> (\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
apply(cases "cast character_data_ptr \<noteq> node_ptr")
by(auto simp add: put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def
NodeMonad.get_M_defs preserved_def split: option.splits bind_splits
dest: get_heap_E)
lemma CharacterData_simp10 [simp]:
"cast character_data_ptr \<noteq> node_ptr
\<Longrightarrow> h \<turnstile> put_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr getter) h h'"
by(auto simp add: NodeMonad.put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def NodeMonad.get_M_defs
preserved_def split: option.splits dest: get_heap_E)
lemma CharacterData_simp11 [simp]:
"cast character_data_ptr \<noteq> object_ptr
\<Longrightarrow> h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
by(auto simp add: put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def
ObjectMonad.get_M_defs preserved_def
split: option.splits dest: get_heap_E)
lemma CharacterData_simp12 [simp]:
"h \<turnstile> put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> (\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
apply(cases "cast character_data_ptr \<noteq> object_ptr")
apply(auto simp add: put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def
get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def ObjectMonad.get_M_defs preserved_def
split: option.splits bind_splits dest: get_heap_E)[1]
by(auto simp add: put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def
get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def ObjectMonad.get_M_defs preserved_def
split: option.splits bind_splits dest: get_heap_E)[1]
lemma CharacterData_simp13 [simp]:
"cast character_data_ptr \<noteq> object_ptr \<Longrightarrow> h \<turnstile> put_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr setter v \<rightarrow>\<^sub>h h'
\<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr getter) h h'"
by(auto simp add: ObjectMonad.put_M_defs get_M_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
ObjectMonad.get_M_defs preserved_def split: option.splits dest: get_heap_E)
lemma new_element_get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a:
"h \<turnstile> new_element \<rightarrow>\<^sub>h h' \<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a ptr getter) h h'"
by(auto simp add: new_element_def get_M_defs preserved_def split: prod.splits option.splits
elim!: bind_returns_result_E bind_returns_heap_E)
subsection\<open>Creating CharacterData\<close>
definition new_character_data :: "(_, (_) character_data_ptr) dom_prog"
where
"new_character_data = do {
h \<leftarrow> get_heap;
(new_ptr, h') \<leftarrow> return (new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a h);
return_heap h';
return new_ptr
}"
lemma new_character_data_ok [simp]:
"h \<turnstile> ok new_character_data"
by(auto simp add: new_character_data_def split: prod.splits)
lemma new_character_data_ptr_in_heap:
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
shows "new_character_data_ptr |\<in>| character_data_ptr_kinds h'"
using assms
unfolding new_character_data_def
by(auto simp add: new_character_data_def new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def Let_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ptr_in_heap
is_OK_returns_result_I
elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_ptr_not_in_heap:
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
shows "new_character_data_ptr |\<notin>| character_data_ptr_kinds h"
using assms new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ptr_not_in_heap
by(auto simp add: new_character_data_def split: prod.splits
elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_new_ptr:
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
shows "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|cast new_character_data_ptr|}"
using assms new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_new_ptr
by(auto simp add: new_character_data_def split: prod.splits
elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_is_character_data_ptr:
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
shows "is_character_data_ptr new_character_data_ptr"
using assms new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_is_character_data_ptr
by(auto simp add: new_character_data_def elim!: bind_returns_result_E split: prod.splits)
lemma new_character_data_child_nodes:
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
shows "h' \<turnstile> get_M new_character_data_ptr val \<rightarrow>\<^sub>r ''''"
using assms
by(auto simp add: get_M_defs new_character_data_def new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def Let_def
split: option.splits prod.splits elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t:
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
\<Longrightarrow> ptr \<noteq> cast new_character_data_ptr \<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr getter) h h'"
by(auto simp add: new_character_data_def ObjectMonad.get_M_defs preserved_def
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e:
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
\<Longrightarrow> ptr \<noteq> cast new_character_data_ptr \<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr getter) h h'"
by(auto simp add: new_character_data_def NodeMonad.get_M_defs preserved_def
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t:
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
\<Longrightarrow> preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr getter) h h'"
by(auto simp add: new_character_data_def ElementMonad.get_M_defs preserved_def
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
lemma new_character_data_get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a:
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
\<Longrightarrow> ptr \<noteq> new_character_data_ptr \<Longrightarrow> preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a ptr getter) h h'"
by(auto simp add: new_character_data_def get_M_defs preserved_def
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
subsection\<open>Modified Heaps\<close>
lemma get_CharacterData_ptr_simp [simp]:
"get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)
= (if ptr = cast character_data_ptr then cast obj else get character_data_ptr h)"
by(auto simp add: get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def split: option.splits Option.bind_splits)
lemma Character_data_ptr_kinds_simp [simp]:
"character_data_ptr_kinds (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h) = character_data_ptr_kinds h |\<union>|
(if is_character_data_ptr_kind ptr then {|the (cast ptr)|} else {||})"
by(auto simp add: character_data_ptr_kinds_def is_node_ptr_kind_def split: option.splits)
lemma type_wf_put_I:
assumes "type_wf h"
assumes "ElementClass.type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
assumes "is_character_data_ptr_kind ptr \<Longrightarrow> is_character_data_kind obj"
shows "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
using assms
by(auto simp add: type_wf_defs split: option.splits)
lemma type_wf_put_ptr_not_in_heap_E:
assumes "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
assumes "ptr |\<notin>| object_ptr_kinds h"
shows "type_wf h"
using assms
apply(auto simp add: type_wf_defs elim!: ElementMonad.type_wf_put_ptr_not_in_heap_E
split: option.splits if_splits)[1]
using assms(2) node_ptr_kinds_commutes by blast
lemma type_wf_put_ptr_in_heap_E:
assumes "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
assumes "ptr |\<in>| object_ptr_kinds h"
assumes "ElementClass.type_wf h"
assumes "is_character_data_ptr_kind ptr \<Longrightarrow> is_character_data_kind (the (get ptr h))"
shows "type_wf h"
using assms
apply(auto simp add: type_wf_defs split: option.splits if_splits)[1]
by (metis (no_types, lifting) ElementClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf assms(2) bind.bind_lunit
cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_inv cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_inv get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def notin_fset option.collapse)
subsection\<open>Preserving Types\<close>
lemma new_element_type_wf_preserved [simp]:
assumes "h \<turnstile> new_element \<rightarrow>\<^sub>h h'"
shows "type_wf h = type_wf h'"
using assms
apply(auto simp add: new_element_def new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
elim!: bind_returns_heap_E type_wf_put_ptr_not_in_heap_E
intro!: type_wf_put_I split: if_splits)[1]
using CharacterDataClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t assms new_element_type_wf_preserved apply blast
using element_ptrs_def apply fastforce
using CharacterDataClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t assms new_element_type_wf_preserved apply blast
by (metis Suc_n_not_le_n element_ptr.sel(1) element_ptrs_def fMax_ge ffmember_filter
fimage_eqI is_element_ptr_ref)
lemma new_element_is_l_new_element: "l_new_element type_wf"
using l_new_element.intro new_element_type_wf_preserved
by blast
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_name_type_wf_preserved [simp]:
"h \<turnstile> put_M element_ptr tag_name_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
dest!: get_heap_E
elim!: bind_returns_heap_E2
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
ObjectMonad.type_wf_put_I)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
apply (metis finite_set_in)
done
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_child_nodes_type_wf_preserved [simp]:
"h \<turnstile> put_M element_ptr child_nodes_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
dest!: get_heap_E elim!: bind_returns_heap_E2
intro!: type_wf_put_I ElementMonad.type_wf_put_I
NodeMonad.type_wf_put_I ObjectMonad.type_wf_put_I)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs
split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs
split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs
split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs
split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs
split: option.splits)[1]
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
apply (metis finite_set_in)
done
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_attrs_type_wf_preserved [simp]:
"h \<turnstile> put_M element_ptr attrs_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
dest!: get_heap_E
elim!: bind_returns_heap_E2
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
ObjectMonad.type_wf_put_I)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
apply (metis finite_set_in)
done
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_shadow_root_opt_type_wf_preserved [simp]:
"h \<turnstile> put_M element_ptr shadow_root_opt_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
dest!: get_heap_E
elim!: bind_returns_heap_E2
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
ObjectMonad.type_wf_put_I)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
ElementMonad.get_M_defs split: option.splits)[1]
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
apply (metis finite_set_in)
done
lemma new_character_data_type_wf_preserved [simp]:
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: new_character_data_def new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def Let_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
elim!: bind_returns_heap_E type_wf_put_ptr_not_in_heap_E
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I ObjectMonad.type_wf_put_I
split: if_splits)[1]
apply(simp_all add: type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs is_node_kind_def)
by (meson new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ptr_not_in_heap)
locale l_new_character_data = l_type_wf +
assumes new_character_data_types_preserved: "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
lemma new_character_data_is_l_new_character_data: "l_new_character_data type_wf"
using l_new_character_data.intro new_character_data_type_wf_preserved
by blast
lemma put_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_val_type_wf_preserved [simp]:
"h \<turnstile> put_M character_data_ptr val_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
apply(auto simp add: CharacterDataMonad.put_M_defs put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
CharacterDataClass.type_wf\<^sub>N\<^sub>o\<^sub>d\<^sub>e CharacterDataClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t
is_node_kind_def
dest!: get_heap_E
elim!: bind_returns_heap_E2
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
ObjectMonad.type_wf_put_I)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs CharacterDataMonad.get_M_defs
split: option.splits)[1]
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs CharacterDataMonad.get_M_defs
ObjectClass.a_type_wf_def
split: option.splits)[1]
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def)
apply (metis finite_set_in)
done
lemma character_data_ptr_kinds_small:
assumes "\<And>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
shows "character_data_ptr_kinds h = character_data_ptr_kinds h'"
by(simp add: character_data_ptr_kinds_def node_ptr_kinds_def preserved_def
object_ptr_kinds_preserved_small[OF assms])
lemma character_data_ptr_kinds_preserved:
assumes "writes SW setter h h'"
assumes "h \<turnstile> setter \<rightarrow>\<^sub>h h'"
assumes "\<And>h h'. \<forall>w \<in> SW. h \<turnstile> w \<rightarrow>\<^sub>h h'
\<longrightarrow> (\<forall>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h')"
shows "character_data_ptr_kinds h = character_data_ptr_kinds h'"
using writes_small_big[OF assms]
apply(simp add: reflp_def transp_def preserved_def character_data_ptr_kinds_def)
by (metis assms node_ptr_kinds_preserved)
lemma type_wf_preserved_small:
assumes "\<And>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
assumes "\<And>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
assumes "\<And>element_ptr. preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr RElement.nothing) h h'"
assumes "\<And>character_data_ptr. preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr
RCharacterData.nothing) h h'"
shows "type_wf h = type_wf h'"
using type_wf_preserved_small[OF assms(1) assms(2) assms(3)]
allI[OF assms(4), of id, simplified] character_data_ptr_kinds_small[OF assms(1)]
apply(auto simp add: type_wf_defs preserved_def get_M_defs character_data_ptr_kinds_small[OF assms(1)]
split: option.splits)[1]
apply(force)
by force
lemma type_wf_preserved:
assumes "writes SW setter h h'"
assumes "h \<turnstile> setter \<rightarrow>\<^sub>h h'"
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
\<Longrightarrow> \<forall>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
\<Longrightarrow> \<forall>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
\<Longrightarrow> \<forall>element_ptr. preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr RElement.nothing) h h'"
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
\<Longrightarrow> \<forall>character_data_ptr. preserved (get_M\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr
RCharacterData.nothing) h h'"
shows "type_wf h = type_wf h'"
proof -
have "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
using assms type_wf_preserved_small by fast
with assms(1) assms(2) show ?thesis
apply(rule writes_small_big)
by(auto simp add: reflp_def transp_def)
qed
lemma type_wf_drop: "type_wf h \<Longrightarrow> type_wf (Heap (fmdrop ptr (the_heap h)))"
apply(auto simp add: type_wf_def ElementMonad.type_wf_drop
l_type_wf_def\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a.a_type_wf_def)[1]
using type_wf_drop
by (metis (no_types, lifting) ElementClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ObjectClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf
character_data_ptr_kinds_commutes finite_set_in fmlookup_drop get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def node_ptr_kinds_commutes object_ptr_kinds_code5)
end